Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of Notes

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              <pb o="404" file="0120" n="128" rhead="CHR. HUG. ILL. QUOR. PROB. CONSTR."/>
            verò reliquam in infinitum licet utrimque productam in diver-
              <lb/>
            ſum curvari; </s>
            <s xml:id="echoid-s2631" xml:space="preserve">quæſitum eſt qua ratione puncta ea determinari
              <lb/>
            poſſent ubi contraria flexio initium capit. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">Et nos quidem ad
              <lb/>
            hoc ſequentem invenimus conſtructionem.</s>
            <s xml:id="echoid-s2633" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2634" xml:space="preserve">Sit duabus A G, A Q tertia proportionalis A E, ſumenda
              <lb/>
            verſus G. </s>
            <s xml:id="echoid-s2635" xml:space="preserve">Et ponatur G F æqualis G E. </s>
            <s xml:id="echoid-s2636" xml:space="preserve">Porro ſit G R ipſi G Q
              <lb/>
            ad angulos rectos, & </s>
            <s xml:id="echoid-s2637" xml:space="preserve">æqualis duplæ G A. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">Et deſcribatur pa-
              <lb/>
            rabole R O, cujus vertex ſit R axis R G, latus rectum ipſi A G
              <lb/>
            æquale. </s>
            <s xml:id="echoid-s2639" xml:space="preserve">Centro autem F radio F R circumferentia deſcriba-
              <lb/>
            tur, quæ parabolen ſecet in O; </s>
            <s xml:id="echoid-s2640" xml:space="preserve">& </s>
            <s xml:id="echoid-s2641" xml:space="preserve">ducatur O C parallela A B
              <lb/>
            occurratque conchoidi in punctis C, D. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">Hæc erunt puncta
              <lb/>
            quæſita in confinio flexionis contrariæ.</s>
            <s xml:id="echoid-s2643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2644" xml:space="preserve">Iſta autem Univerſalis eſt conſtructio. </s>
            <s xml:id="echoid-s2645" xml:space="preserve">At quando quadra-
              <lb/>
              <note position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">TAB. XLII.
                <lb/>
              Fig. 6.</note>
            tum ex A Q non majus eſt quam duplum quadrati A G, ar-
              <lb/>
            cus triſectione propoſitum quoque efficiemus. </s>
            <s xml:id="echoid-s2646" xml:space="preserve">Et diversè qui-
              <lb/>
            dem prout A Q major vel minor erit quam A G. </s>
            <s xml:id="echoid-s2647" xml:space="preserve">Etenim ſi
              <lb/>
            minor, deſcribenda eſt circumferentia centro A radio A G,
              <lb/>
            in eaque ponenda G K æqualis duplæ G E, inventæ ut priùs.
              <lb/>
            </s>
            <s xml:id="echoid-s2648" xml:space="preserve">Et rectæ G H quæ ſubtendit trientem circumferentiæ K H G
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            æqualis ſumenda G M, & </s>
            <s xml:id="echoid-s2649" xml:space="preserve">per M ducenda ut ante D C ipſi
              <lb/>
              <note position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">TAB. XLII.
                <lb/>
              Fig. 7.</note>
            A B parallela. </s>
            <s xml:id="echoid-s2650" xml:space="preserve">Cum verò A Q major eſt quam A G, cæte-
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            ris ad eundem modum compoſitis, hæc tantum differentia
              <lb/>
            erit quod arcum K P, qui unà cum arcu G K ſemicircum-
              <lb/>
            ferentiam explet, in tria æqualia dividere oportet, & </s>
            <s xml:id="echoid-s2651" xml:space="preserve">partium
              <lb/>
            unam conſtituere P H, & </s>
            <s xml:id="echoid-s2652" xml:space="preserve">ſubtenſæ G H æqualem ſumere G M.</s>
            <s xml:id="echoid-s2653" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2654" xml:space="preserve">Porro planum eſt Problema cum A G æqualis A Q. </s>
            <s xml:id="echoid-s2655" xml:space="preserve">Tunc
              <lb/>
            enim G M fit æqualis lateri trigoni ordinati in circulo in-
              <lb/>
            ſcripti. </s>
            <s xml:id="echoid-s2656" xml:space="preserve">Item cum quadratum A Q duplum eſt quadrati A G:
              <lb/>
            </s>
            <s xml:id="echoid-s2657" xml:space="preserve">fit enim G M dupla ipſius G A.</s>
            <s xml:id="echoid-s2658" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s2659" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s2660" xml:space="preserve">aliis caſibus innumeris planum erit, quorum ii qui-
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            dem facilè diſcerni poterunt, qui ad anguli triſectionem re-
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            ducuntur.</s>
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          </p>
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          <head xml:id="echoid-head89" style="it" xml:space="preserve">FINIS.</head>
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